The main topic of this talk is the speed estimation of stability/instability. The word “various” comes with no surprising since there are a lot of different types of stability/instability and each of them has its own natural distance to measure. However, the adjective “unified” is very much unexpected. The talk surveys our recent progress on the topic, made in the past five years or so.
@article{bwmeta1.element.doi-10_1515_spma-2016-0002,
author = {Mu-Fa Chen},
title = {Unified speed estimation of various stabilities},
journal = {Special Matrices},
volume = {4},
year = {2016},
pages = {9-12},
zbl = {1338.60186},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2016-0002}
}
Mu-Fa Chen. Unified speed estimation of various stabilities. Special Matrices, Tome 4 (2016) pp. 9-12. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2016-0002/
[1] Chen, M.F. (2003). Variational formulas of Poincaré-type inequalities for birth-death processes. Acta Math. Sin. Eng. Ser. 19(4): 625-644.[Crossref] | Zbl 1040.60064
[2] Chen, M.F. (2004). From Markov Chains to Non-equilibrium Particle Systems. World Scientific. 2nd ed. (1st ed., 1992).
[3] Chen, M.F. (2005). Eigenvalues, Inequalities, and Ergodic Theory. Springer, London. | Zbl 1079.60005
[4] Chen, M.F. (2007). Exponential convergence rate in entropy. Front. Math. China, 2(3): 329–358.[Crossref] | Zbl 1152.60059
[5] Chen M.F. (2010). Speed of stability for birth–death processes. Front Math China 5(3): 379–515.
[6] Chen, M.F. (2012). Lower bounds of principal eigenvalue in dimension one. Front. Math. China 7(4): 645–668.[WoS][Crossref] | Zbl 1263.34122
[7] Chen, M.F. (2013a). Bilateral Hardy-type inequalities. Acta Math Sin Eng Ser. 29(1): 1–32.[Crossref] | Zbl 1263.26028
[8] Chen, M.F. (2013b). Bilateral Hardy-type inequalities and application to geometry. Mathmedia 37(2): 12–32; Math. Bulletin 52(8/9) (in Chinese).
[9] Chen, M.F. (2014). Criteria for discrete spectrum of 1D operators. Commu. Math. Stat. 2: 279–309[Crossref] | Zbl 1309.47005
[10] Chen, M.F. (2015a). Criteria for two spectral problems of 1D operators (in Chinese). Sci Sin Math, 44(1):
[11] Chen, M.F. (2015b). The optimal constant in Hardy-type inequalities. Acta Math. Sinica, Eng. Ser.[Crossref][WoS] | Zbl 1318.26035
[12] Chen, M.F. (2015c). Progress on Hardy-type inequalities. Chapter 6 in the book “Festschrift Masatoshi Fukushima”, eds: Z.Q. Chen, N. Jacob, M. Takeda, and T. Uemura, World Sci. | Zbl 1341.42012
[13] Chen, M.F. and Zhang, X. (2014) Isospectral operators. Commu Math Stat 2: 17–32.[Crossref] | Zbl 1310.47047
[14] Liao, Z.W. (2015). Discrete weighted Hardy inequalities with different boundary conditions. arXiv:1508.04601.